Class 6: Maths Chapter 31 solutions. Complete Class 6 Maths Chapter 31 Notes.
Selina Class 6 ICSE Solutions Mathematics : Chapter 31- Recognition of Solids
Selina 6th Maths Chapter 31, Class 6 Maths Chapter 31 solutions
Exercise 31
1. Identify the nets which can be used to form cubes:
Solution:
The net of a cube is the one which has the faces arranged in such a way that it makes a complete cubic structure
(i) In the given figure, the net cannot be folded into a cube by folding the six faces of the net
Therefore, it is not a cube net.
(ii) In the given figure, the net can be folded into a cube when its faces are folded one over the other
Therefore, it is a cube net
(iii) In the given figure, the net can be folded into a cube when its faces are folded one over the other
Therefore, it is a cube net
(iv) In the given figure, the net cannot be folded into a cube by folding the six faces of the net
Therefore, it is not a cube net
(v) In the given figure, the net can be folded into a cube when its faces are folded one over the other
Therefore, it is a cube net
2. Draw at least three different nets for making cube.
Solution:
A cube net is defined as the net in which if all the faces are folded over other, they make up a perfect cube
3. The dimensions of a cuboid are 6 cm, 4 cm and 3 cm. Draw two different types of oblique sketches for this cuboid.
Solution:
A shape with the six faces which has the different values of the length, breadth and height is known as cuboid
(i)
(ii)
4. Two cubes, each with 3 cm edge, are placed side by side to form a cuboid. For this cuboid, draw:
(i) an oblique sketch
(ii) an isometric sketch
Solution:
(i) An oblique sketch of a cuboid is shown below
(ii)An isometric sketch of a cuboid is shown below
5. The figure, given below, shows shadows of some 3D objects, when seen under the lamp of an overhead projector:
In each case, name the object.
Solution:
The following figures are considered to be the image of a 3D object when seen under the lamp of an overhead projector
6. Look at the solids, drawn below, and fill the given chart.
| Polyhedon | Faces (F) | Vertices (V) | Edges (E) | F – E + V |
| (a) Triangular pyramid | ||||
| (b) Square pyramid | ||||
| (c) Hexahedron | ||||
| (d) Hexagonal prism |
Solution:
| Polyhedon | Faces (F) | Vertices (V) | Edges (E) | F – E + V |
| (a) Triangular pyramid | 4588 | 45612 | 681218 | 2222 |
| (b) Square pyramid | ||||
| (c) Hexahedron | ||||
| (d) Hexagonal prism |
(i) A triangular pyramid has,
Number of faces = 4
Number of edges = 6
Number of vertices = 4
Hence,
F – E + V = 4 – 6 + 4
= – 2 + 4
= 2
(ii) A square pyramid has,
Number of faces = 5
Number of edges = 8
Number of vertices = 5
Hence,
F – E + V = 5 – 8 + 5
= – 3 + 5
= 2
(iii) A hexahedron has,
Number of faces = 8
Number of edges = 12
Number of vertices = 6
Hence,
F – E + V = 8 – 12 + 6
= – 4 + 6
= 2
(iv) A hexagonal prism has,
Number of faces = 8
Number of edges = 18
Number of vertices = 12
Hence,
F – E + V = 8 – 18 + 12
= – 10 + 12
= 2
7. Dice are cubes with dot or dots on each face. Opposite faces of a die always have a total of seven on them.
Below are given two nets to make dice (cube), the numbers inserted in each square indicate the number of dots in it.
Insert suitable numbers in each blank so that numbers in opposite faces of the die have a total of seven dots.
Solution:
Following are the figures where the numbers are inserted such that the numbers in opposite faces of the die have a total of seven dots
In the given cube net, 4 lies opposite to 3, 6 lies opposite to 1 and 5 lies opposite to 2
In the given cube net, 4 lies opposite to 3, 6 lies opposite to 1 and 5 lies opposite to 2
8. The following figure represents nets of some solids. Name the solids.
Solution:
The names of the solids, which represent nets of the above figures, are as follows:
(i) Tetrahedron
(ii) Triangular prism
(iii) Cube
(iv) Cuboid
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Selina Class 6 ICSE Solutions Mathematics : Chapter 31- Recognition of Solids
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Chapterwise Selina Publishers ICSE Solutions for Class 6 Mathematics :
- Chapter 1- Number System
- Chapter 2- Estimation
- Chapter 3- Numbers In Indian And International Systems
- Chapter 4- Place Value
- Chapter 5- Natural Numbers And Whole Numbers
- Chapter 6- Negative Numbers And Integers
- Chapter 7- Number Line
- Chapter 8- HCF And LCM
- Chapter 9- Playing With Numbers
- Chapter 10- Sets
- Chapter 11- Ratio
- Chapter 12- Proportion
- Chapter 13- Unitary Method
- Chapter 14- Fractions
- Chapter 15- Decimal Fractions
- Chapter 16- Percent (Percentage)
- Chapter 17- Idea of Speed, Distance and Time
- Chapter 18- Fundamental Concepts
- Chapter 19- Fundamental Operations
- Chapter 20- Substitution
- Chapter 21- Framing Algebraic Expressions (Including Evaluation)
- Chapter 22- Simple (Linear) Equations
- Chapter 23- Fundamental Concepts
- Chapter 24- Angles
- Chapter 25- Properties of Angles and Lines
- Chapter 26- Triangles
- Chapter 27- Quadrilateral
- Chapter 28- Polygons
- Chapter 29- The Circle
- Chapter 30- Revision Exercise Symmetry
- Chapter 31- Recognition of Solids
- Chapter 32- Perimeter and Area of Plane Figures
- Chapter 33- Data Handling
- Chapter 34- Mean and Median
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